%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU532^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:35:07 AM UTC 2026
% Result : Theorem 1.51s 1.27s
% Output : Refutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 90 ( 19 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 131 ( 8 ~; 0 |; 2 &; 108 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 6 usr; 7 con; 0-2 aty)
% ( 8 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 32 ( 10 ^; 18 !; 4 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(f20,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f14,f19]) ).
thf(f19,plain,
! [X2: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] : ( in @ X1 @ ( setadjoin @ X1 @ Y0 ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] : ( in @ X1 @ ( setadjoin @ X1 @ Y0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f13,f12]) ).
thf(f12,plain,
( setadjoinIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( setadjoinIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
( setadjoinIL
= ( ! [X0: $i,X1: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( setadjoinIL
= ( ! [X1: $i,X0: $i] : ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zncl78ptFD/DTF2THF_4740.p',setadjoinIL) ).
thf(f13,plain,
setadjoinIL = $true,
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( $true
!= ( in @ sK1 @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) ) )
& ( setadjoinIL = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f10]) ).
thf(f10,plain,
( ? [X0: $i,X1: $i] :
( $true
!= ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) )
=> ( $true
!= ( in @ sK1 @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ? [X0: $i,X1: $i] :
( $true
!= ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) )
& ( setadjoinIL = $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( setadjoinIL = $true )
=> ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( setadjoinIL
=> ! [X0: $i,X1: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( setadjoinIL
=> ! [X1: $i,X0: $i] : ( in @ X0 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( setadjoinIL
=> ! [X1: $i,X0: $i] : ( in @ X0 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zncl78ptFD/DTF2THF_4740.p',upairsetIL) ).
thf(f14,plain,
( $true
!= ( in @ sK1 @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU532^2 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n016.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 12:26:36 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : SEU532^2 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.46 % Domain : Set Theory
% 0.20/0.46 % Problem : Preliminary Notions - Equality Laws
% 0.20/0.46 % Version : Especial > Reduced > Especial.
% 0.20/0.46 % English : (! x:i.! y:i.in x (setadjoin x (setadjoin y emptyset)))
% 0.20/0.46
% 0.20/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.20/0.46 % Source : [Bro08]
% 0.20/0.46 % Names : ZFC034l [Bro08]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.20/0.46 % Syntax : Number of formulae : 6 ( 1 unt; 4 typ; 1 def)
% 0.20/0.46 % Number of atoms : 5 ( 1 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 2 ( 2 avg)
% 0.20/0.46 % Number of connectives : 11 ( 0 ~; 0 |; 0 &; 10 @)
% 0.20/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 8 ( 5 avg)
% 0.20/0.46 % Number of types : 2 ( 0 usr)
% 0.20/0.46 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 5 ( 4 usr; 2 con; 0-2 aty)
% 0.20/0.46 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.20/0.46 % SPC : TH0_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : http://mathgate.info/detsetitem.php?id=505
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 thf(in_type,type,
% 0.20/0.46 in: $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptyset_type,type,
% 0.20/0.46 emptyset: $i ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoin_type,type,
% 0.20/0.46 setadjoin: $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinIL_type,type,
% 0.20/0.46 setadjoinIL: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinIL,definition,
% 0.20/0.46 ( setadjoinIL
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(upairsetIL,conjecture,
% 0.20/0.46 ( setadjoinIL
% 0.20/0.46 => ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 1.51/1.24 ---- Embedded in THF ---
% 1.51/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.51/1.24 %%% Generated on Tue Feb 24 12:26:36 EST 2026
% 1.51/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.51/1.24 %%% Logic specification used:
% 1.51/1.24 %%% thf(spec, logic, $$dhol).
% 1.51/1.24
% 1.51/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.zncl78ptFD/DTF2DTF4740.p
% See solution above
% 1.51/1.24 ------------------------
% 1.51/1.25 ---- Cleaned THF ---
% 1.51/1.25 thf(in_type,type,
% 1.51/1.25 in: $i > $i > $o ).
% 1.51/1.25
% 1.51/1.25 thf(emptyset_type,type,
% 1.51/1.25 emptyset: $i ).
% 1.51/1.25
% 1.51/1.25 thf(setadjoin_type,type,
% 1.51/1.25 setadjoin: $i > $i > $i ).
% 1.51/1.25
% 1.51/1.25 thf(setadjoinIL_type,type,
% 1.51/1.25 setadjoinIL: $o ).
% 1.51/1.25
% 1.51/1.25 thf(setadjoinIL,definition,
% 1.51/1.25 ( setadjoinIL
% 1.51/1.25 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 1.51/1.25
% 1.51/1.25 thf(upairsetIL,conjecture,
% 1.51/1.25 ( setadjoinIL
% 1.51/1.25 => ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ).
% 1.51/1.25 ------------------------
% 1.51/1.27 % (4930)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4740 for (2999ds/183Mi)
% 1.51/1.27 % (4934)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_4740 for (2999ds/2Mi)
% 1.51/1.27 % (4932)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_4740 for (2999ds/27Mi)
% 1.51/1.27 % (4930)First to succeed.
% 1.51/1.27 % (4934)Instruction limit reached!
% 1.51/1.27 % (4934)------------------------------
% 1.51/1.27 % (4934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.27 % (4934)Termination reason: Unknown
% 1.51/1.27 % (4934)Termination phase: Saturation
% 1.51/1.27
% 1.51/1.27 % (4934)Memory used [KB]: 5500
% 1.51/1.27 % (4934)Time elapsed: 0.002 s
% 1.51/1.27 % (4934)Instructions burned: 2 (million)
% 1.51/1.27 % (4934)------------------------------
% 1.51/1.27 % (4934)------------------------------
% 1.51/1.27 % (4932)Also succeeded, but the first one will report.
% 1.51/1.27 % (4930)Refutation found. Thanks to Tanya!
% 1.51/1.27 % SZS status Theorem for DTF2THF_4740
% 1.51/1.27 % SZS output start Proof for DTF2THF_4740
% 1.51/1.27 thf(func_def_0, type, in: $i > $i > $o).
% 1.51/1.27 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.51/1.27 thf(f20,plain,(
% 1.51/1.27 $false),
% 1.51/1.27 inference(subsumption_resolution,[status(thm)],[f14,f19])).
% 1.51/1.27 thf(f19,plain,(
% 1.51/1.27 ( ! [X2 : $i,X1 : $i] : (($true = (in @ X1 @ (setadjoin @ X1 @ X2)))) )),
% 1.51/1.27 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.51/1.27 thf(f18,plain,(
% 1.51/1.27 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (in @ X1 @ (setadjoin @ X1 @ Y0))) @ X2) = $true)) )),
% 1.51/1.27 inference(pi_clausification,[status(thm)],[f17])).
% 1.51/1.27 thf(f17,plain,(
% 1.51/1.27 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (in @ X1 @ (setadjoin @ X1 @ Y0)))) = $true)) )),
% 1.51/1.27 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.51/1.27 thf(f16,plain,(
% 1.51/1.27 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1))))) @ X1) = $true)) )),
% 1.51/1.27 inference(pi_clausification,[status(thm)],[f15])).
% 1.51/1.27 thf(f15,plain,(
% 1.51/1.27 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) = $true)),
% 1.51/1.27 inference(definition_unfolding,[status(thm)],[f13,f12])).
% 1.51/1.27 thf(f12,plain,(
% 1.51/1.27 (setadjoinIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))))),
% 1.51/1.27 inference(cnf_transformation,[status(thm)],[f6])).
% 1.51/1.27 thf(f6,plain,(
% 1.51/1.27 (setadjoinIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))))),
% 1.51/1.27 inference(fool_elimination,[status(thm)],[f5])).
% 1.51/1.27 thf(f5,plain,(
% 1.51/1.27 (setadjoinIL = ! [X0 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X1 @ X0)))),
% 1.51/1.27 inference(rectify,[status(thm)],[f1])).
% 1.51/1.27 thf(f1,axiom,(
% 1.51/1.27 (setadjoinIL = ! [X1 : $i,X0 : $i] : (in @ X0 @ (setadjoin @ X0 @ X1)))),
% 1.51/1.27 file('/export/starexec/sandbox/tmp/tmp.zncl78ptFD/DTF2THF_4740.p',setadjoinIL)).
% 1.51/1.27 thf(f13,plain,(
% 1.51/1.27 (setadjoinIL = $true)),
% 1.51/1.27 inference(cnf_transformation,[status(thm)],[f11])).
% 1.51/1.27 thf(f11,plain,(
% 1.51/1.27 ($true != (in @ sK1 @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)))) & (setadjoinIL = $true)),
% 1.51/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f10])).
% 1.51/1.27 thf(f10,plain,(
% 1.51/1.27 ? [X0 : $i,X1 : $i] : ($true != (in @ X1 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)))) => ($true != (in @ sK1 @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset))))),
% 1.51/1.27 introduced(definition,[],[choice_axiom])).
% 1.51/1.27 thf(f9,plain,(
% 1.51/1.27 ? [X0 : $i,X1 : $i] : ($true != (in @ X1 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)))) & (setadjoinIL = $true)),
% 1.51/1.27 inference(ennf_transformation,[status(thm)],[f8])).
% 1.51/1.27 thf(f8,plain,(
% 1.51/1.27 ~((setadjoinIL = $true) => ! [X0 : $i,X1 : $i] : ($true = (in @ X1 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)))))),
% 1.51/1.27 inference(fool_elimination,[status(thm)],[f7])).
% 1.51/1.27 thf(f7,plain,(
% 1.51/1.27 ~(setadjoinIL => ! [X0 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))))),
% 1.51/1.27 inference(rectify,[status(thm)],[f3])).
% 1.51/1.27 thf(f3,negated_conjecture,(
% 1.51/1.27 ~(setadjoinIL => ! [X1 : $i,X0 : $i] : (in @ X0 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))))),
% 1.51/1.27 inference(negated_conjecture,[status(cth)],[f2])).
% 1.51/1.27 thf(f2,conjecture,(
% 1.51/1.27 setadjoinIL => ! [X1 : $i,X0 : $i] : (in @ X0 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)))),
% 1.51/1.27 file('/export/starexec/sandbox/tmp/tmp.zncl78ptFD/DTF2THF_4740.p',upairsetIL)).
% 1.51/1.27 thf(f14,plain,(
% 1.51/1.27 ($true != (in @ sK1 @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset))))),
% 1.51/1.27 inference(cnf_transformation,[status(thm)],[f11])).
% 1.51/1.27 % SZS output end Proof for DTF2THF_4740
% 1.51/1.27 % (4930)------------------------------
% 1.51/1.27 % (4930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.27 % (4930)Termination reason: Refutation
% 1.51/1.27
% 1.51/1.27 % (4930)Memory used [KB]: 5500
% 1.51/1.27 % (4930)Time elapsed: 0.002 s
% 1.51/1.27 % (4930)Instructions burned: 2 (million)
% 1.51/1.27 % (4930)------------------------------
% 1.51/1.27 % (4930)------------------------------
% 1.51/1.27 % (4929)Success in time 0.012 s
%------------------------------------------------------------------------------